oecd cyclical analysis and composite indicators system

Organisation for Economic Co-operation and Development Organisation de Coopération et de Développement Économiques

STATISTICS DIRECTORATE

SHORT-TERM ECONOMIC STATISTICS DIVISION

OECD

CYCLICAL ANALYSIS AND

COMPOSITE INDICATORS SYSTEM

USER GUIDE

VERSION 3

PARIS 2005

OECD Cyclical Analysis and Composite Indicators System: User Guide 2

TABLE OF CONTENTS

1. INTRODUCTION..................................................................................................................... 4

1.1. Installation of the software.................................................................................................. 5 1.2. Presentation of the software................................................................................................ 5 1.3. Format of input files............................................................................................................ 8

2. CYCLICAL ANALYSIS ........................................................................................................ 11

2.1. “Implementation of the Project” procedure ...................................................................... 12 2.2. “Launch Complete Study” procedure ............................................................................... 17

2.2.1. Reference series.......................................................................................................... 19 2.2.2. Quarterly series........................................................................................................... 20 2.2.3. Manual turning points ................................................................................................ 21 2.2.4. Turning points with Hodrick-Prescott ........................................................................ 22 2.2.5. The Results file........................................................................................................... 25 2.2.6. Implication in the directories...................................................................................... 25

2.3. “Change Options to Indicators” procedure ....................................................................... 26 2.3.1. View and Change Options.......................................................................................... 27 2.3.2. Series in the study....................................................................................................... 29 2.3.3. Change beginning date ............................................................................................... 30 2.3.4. Add component(s) ...................................................................................................... 31

2.4. “Graph of turning points procedure” procedure................................................................ 32 2.5. “Compilation of Statistics” procedure .............................................................................. 33

2.5.1. Graphs ........................................................................................................................ 34 2.5.2. Cross-correlation ........................................................................................................ 35 2.5.3. Statistical board (called StatBoard) ............................................................................ 36

2.6. “Compilation of Final Statistical Boards” procedure........................................................ 36 2.7. “View of Final Cyclical Analysis Results” procedure...................................................... 38 2.8. “Go to COMPOSITE INDICATOR SYSTEM” procedure.............................................. 39

3. COMPOSITE INDICATORS ................................................................................................. 40

3.1. “Creation a new Composite Indicator” procedure ............................................................ 41 3.2. “View of a Created Composite Indicator” procedure ....................................................... 45 3.3. “View of Turning Points” procedure ................................................................................ 46 3.4. “Compilation of Statistics” procedure .............................................................................. 47 3.5. “Compilation of Final Statistical Boards” procedure........................................................ 48 3.6. “View of Final CI Results” procedure .............................................................................. 49

ANNEX: THE PHASE-AVERAGE TREND PROGRAM – OECD VERSION 4 (2003)......... 51

Objectives............................................................................................................................. 51 Program Outline ................................................................................................................... 51 Turning Points Selection ...................................................................................................... 51 Long-term trend estimation .................................................................................................. 52


Detailed program steps......................................................................................................... 52 Installation............................................................................................................................ 52 Input data file ....................................................................................................................... 53 Output................................................................................................................................... 55 Common problems ............................................................................................................... 56

GLOSSARY................................................................................................................................ 57

Amplitude adjustment .......................................................................................................... 57 Business cycle ...................................................................................................................... 57 Composite Leading Indicator (CLI) ..................................................................................... 57 Component series ................................................................................................................. 57 Cyclical behaviour................................................................................................................ 57 Cycle..................................................................................................................................... 57 Growth cycle ........................................................................................................................ 58 Months for Cyclical Dominance (MCD).............................................................................. 58 Normalisation ....................................................................................................................... 58 One-month percent change................................................................................................... 58 Phase..................................................................................................................................... 58 Quadratic Probability Score (QPS) ...................................................................................... 59 Ratio to trend........................................................................................................................ 59 Reference series.................................................................................................................... 60 Six-month rate of change ..................................................................................................... 60 Smoothing ............................................................................................................................ 60 Trend .................................................................................................................................... 60 Trend-restored ...................................................................................................................... 60 Turning point........................................................................................................................ 60


1. INTRODUCTION

The software is a tool both for cyclical analysis and for the compilation and study of composite indicators.

The cyclical analysis phase aims to define the cyclical behaviour of a chosen set of short-term economic indicators. The analysis requires series which are stationary, i.e. each series should be seasonally adjusted and without trend. The seasonal adjustment should be carried out prior to the cyclical analysis study. The procedure TREND4.exe will then remove the trend component of the series using the Phase-Average-Trend method. At this point we have stationary series, which can then be normalised in order to express the cyclical movements in a comparable form.

The data are then ready for the composite indicators phase. Three tools are available to aid selection of the best input indicators for the compilation of composite indicators. The first is a graphical representation of the indicator and the reference series, the second is the cross correlation between the indicator and the reference series, and the third is the statistical board which calculates the mean lag/lead at turning points, the median lag/lead at turning points and standard deviation between the indicator and the reference series.

With the aid of these tools, a range of composite indicators - lagging, coincident or leading – can be tested. For each composite indicator compiled, the best indicators should be selected manually from the list using the graphs, cross-correlation and statistical board for guidance. The different composite indicators are assessed, and a final procedure allows you to save the most important results of the study in a dedicated file.

This user guide is structured in the same way as the software, i.e. it contains two important parts – the cyclical analysis phase and the composite indicator phase. The procedure TREND4.exe (which compiles the phase-average trend program) is explained in an annex, and the glossary provides a set of relevant definitions.

In order to present this user guide we are going to use a fictitious example called OECDExample. In this example, all possibilities are going to be presented. We will start with a set of two reference series (one monthly and one quarterly), seven monthly series (the set of monthly series is split into two different files in order to demonstrate a specific tool of the software) and three quarterly series (one series has been duplicated with two different names – the reason will be explained further).

The software is linked to a seasonal adjustment software called DEMETRA and developed by EUROSTAT. As stationary series are needed, the seasonal adjustment procedure is done with DEMETRA before the beginning of a study.


1.1. Installation of the software

The software is composed of two files:

� PAT.xls � TREND4.exe

First of all, you must create the directory OECD_CACIS under your C:\ drive. Then, on C:\OECD_CACIS\, the two above files must be copied before processing any study. After, that, a quick procedure is to create a shortcut of PAT.xls on your desktop (under C:\OECD_CACIS\, click with the right button on PAT.xls and then select Send To and then Desktop (create shortcut).

Concerning the configuration of the screen, in order to be able to see the software in your whole screen, you need at least the screen resolution at 1152 by 864 pixels. For this, go to control panel, then select Display Properties then go to Settings and under Screen Resolution select 1152 x 864 pixels.

1.2. Presentation of the software

When you open the PAT.xls file, the following window appears:


Two choices are possible:

1. Create a New Project:

By clicking on “Create a New Project”, the following window appears:

After clicking on OK, the PAT.xls file is renamed with the following name PAT_NameOfProject.xls. In this example the name of the new project is now PAT_OECDExample.xls. When looking at the Windows NT Explorer under C:\OECD_CACIS\, the sub-directory OECDExample has been created. So, it is possible to have an unlimited number of projects.

If you want to create a new project and the project name you give already exists, the following message will appear and a new name must be entered:

2. Open Existing Project

By clicking on this button, the software proposes a scroll bar choice in order to select the project to be open:


If you have only one created project, the scroll bar box does not appear and the project is automatically open.

The software is composed of two different parts in order to separate the cyclical analysis and the composite indicators system:

1. Cyclical Analysis

This part includes the study of the cyclical behaviour of short-term economic indicators on a monthly or a quarterly basis. The aim is to compare the cyclical behaviour of indicators to one or several reference series:


2. Composite Indicators System

This part includes the possibility of constructing composite indicators from the list of indicators of the previous part “Cyclical Analysis”.

On each part (cyclical analysis and composite indicator system), if you click on the OECD logo, you directly reach the OECD website on Composite Leading Indicators.

1.3. Format of input files

Series with different frequencies must be presented in separate input files i.e. monthly data in one file, and quarterly data in a second file. Thus, it is common to have two input files. In each file, the first column must contain the dates (format should be a date format) and the remaining columns the series you want to treat. The first line must contain the title of the series. Titles are very important because we will keep them throughout the study; so, it is important to have logical titles. A series name must not have the same name as an input data file name (without its extension).

Here is an example of data presentation and titles for series of monthly data:


For quarterly series, the first quarter is labelled January, the second April, the third July and the fourth October (this is because the seasonal adjustment has been performed with Demetra).


For both files with monthly data and quarterly data, you can notice the presence of five sheets that can be needed for a study. These sheets (except Sheet1) have been created after having processed the seasonal adjustments and the compilation of business cycles with the Hodrick-Prescott method in DEMETRA using the Tramo/Seats program for seasonal adjustment. Here is the explanation of all sheets included in each data file: � Sheet1 (for example) includes the original data � Demetra_Parameters includes all parameters defined for treatment of time series (using X-12

ARIMA or Tramo/Seats) � Demetra_Results_fa includes all final seasonally adjusted series series (using X-12 ARIMA or

Tramo/Seats) � Demetra_Results_b includes all business cycles from Hodrick-Prescott filter using Tramo/Seats � Demetra_Results_fl includes all final long-term trend from Hodrick-Prescott filter using

Tramo/Seats If the seasonal adjustment procedure is not compiled with DEMETRA, the easy way to run PAT.xls is to rename the sheet where all seasonally adjusted series are to Demetra_Results_fa.

Seasonal adjustment, trend and cycle estimation with DEMETRA using Tramo/Seats program must respect the following minimum steps for execution of automatic run:

� Select Automated Mode � Select Excel Input Data File � Save Final Seasonal Adjusted Series (.fa) � Save Business Cycle from HP (.b) � Save Final Long-term Trend from HP (.fl) � Statistical Tool – Select Customised Parameters for a New Processing � Select Tramo/Seats as Seasonal Adjustment Method � Select No Automatic Outlier Detection and Correction If you do not need to process in the study the Hodrick-Prescott method (so you will use only TREND4.exe to de-trend the indicators), it is not necessary to save the two following sheets in Demetra – Demetra_Results_b and Demetra_Results_fl.

N.B.: � For all series whether they are monthly or quarterly, the series must begin in January for a

monthly series and in Q1 (labelled January) for a quarterly series (a checking control has been implemented).

� You must not have missing values in your series. If so, the time series taken by the software will stop at the missing data point.

� You must not have a space after the name of a series in your excel sheet (frequent error which is very hard to detect).

� The name of an Excel file must not have the same name as a series in the file. � The configuration of your PC must be like the English one. For example, data must be 126.3

(English configuration) but cannot be 126,3 (French configuration). � You must have a C:\ drive


2. CYCLICAL ANALYSIS

Now, let us investigate how to use the cyclical analysis part of the software. The remainder of this document presents all steps needed for compiling composite indicators. The aim of this part is to analyse the cyclical characteristics of the set of economic indicators compared to the selected reference series. For each step, a help button is available.


The cyclical analysis part is composed of eight different steps:

1. Implementation of the Project 2. Launch Complete Study 3. Change Options to Indicators 4. Graphs of Turning Points 5. Compilation of Statistics 6. Compilation of Final Statistical Boards 7. View of Final Cyclical Analysis results 8. Go to Composite Indicator System

2.1. “Implementation of the Project” procedure

This button creates in Windows NT Explorer the sub-directories necessary to compile the composite indicators. First, click on the button – it will ask you how many input data file you have. It is convenient to have one data file for each frequency of the series i.e. monthly and quarterly.

After having entered the number of input files and click on OK, the automatic box “Select One File To Open” appears and then select the file(s) in their directory by double clicking on.


A checking procedure controls whether all time series begin either in January for a monthly series or in Q1 for a quarterly series. If not, the following message below will appear until all time series begin in January or first Quarter:

The correction must be done for all series that have been compiled (at least the seasonally adjusted time series, and potentially the business cycle and the long-term trend series). For the original series, it is not necessary as these series will not be used in the study.

When your file is correct, it is asked for each series to implement some information before their treatment:

� De-trending method: choice between the Phase Average Trend (PAT) method and the Hodrick-Prescott method (if the Hodrick-Prescott method is selected, it is not possible to select the options Deviation from trend, Turning points, De-trending and Print options).

� Reference series or component series: define the series as a reference series or a component series. It is possible to define more than one reference series.

� Inversion of the series: define whether the series should be inverted or not. � Deviation from trend: define the series as ratio-to-trend or difference from trend. Ratio to trend is

used when the underlying structure of the series is multiplicative. Difference from trend is used when the underlying structure of the series is additive or when the series contains negative values.

� Turning points: select if turning points must be compiled automatically or manually. If turning points are calculated automatically, it will be done by Trend4.exe.

� De-trending: select whether the long-term trend must be compiled or not. Business tendency survey series expressed in balance form are in general considered to be without a changing long term trend. This means that such series may be used even if the time series is short.

� Print options: select the print options from a short printout to an extra long printout.


Here is the options screen that must be filled in for each series. Of course at least one series must be defined as a reference series.

With the button “Back” it is possible to come back and change the options for one series. When you enter the options to the last indicator, the button “Next” is replaced by “Final”. By clicking on the button “Final”, the final structure under the sub-directory C:\OECD_CACIS\OECDExample is the following one:


In our example, two reference series have been created (under the sub-direct 1_NameReferenceSeries) and under each reference series, three groups of statistics (CrossCorrelation, Graphs and StatBoard) and a result sub-directory called Results. Under each reference series sub-directory:

� CrossCorrelation contains the cross correlation of the component series with the reference series. � Graphs contains the graphs of the component series with the reference series. � Results contains an Excel file with all result tables. � StatBoard contains the statistical boards of the cyclical characteristics of the component series

with regard to the reference series. If a series is both a reference series and a component series, it is not possible to have one series with these two characteristics (reference series and component series). So, two different series with same data and different names must be created. In our example, the GDP is used as a reference series (series is called Gdp) and as a component series (series is called GdpComponent).

For each component series, a sub-directory has been created under the sub-directory 3_NameComponentSeries.

The sub-directory 4_OriginalData includes the input data file and in our example, two files which are MonthlyData1.xls and QuarterlyData.xls.


If you forget to select an indicator as a reference series, the following window appears and asks you to choose among the complete list of the indicators a reference series:


2.2. “Launch Complete Study” procedure

This step compiles the normalisation for each series. The different steps to compile the normalisation of a series are:

1. Seasonally adjusted series 2. Launch of TREND4.exe to define the long-term trend and turning points 3. Compilation of the difference from trend series (get rid of long-term trend) 4. Determination of the Month for Cyclical Dominance (MCD) value (see definition in Annex) 5. Moving average applied to the difference from trend series depending on the MCD value 6. Normalisation of the MCD series of components by subtracting mean and divide by mean of

absolute values of difference from the mean By clicking on the button “Launch Complete Study”, the following box appears:

It is possible to select either series one by one or all series at once (first possibility: All series). This step will take all the options specified by the step “Implementation of the project” in order to compile the normalised series. Here are all the steps from the beginning to the final normalised series and all possibilities that can be seen following the chosen options:


After running the procedure, in the Results file, the time period available and the MCD/QCD are updated in Table 2, see below:


2.2.1. Reference series

When you run this procedure for the reference series, it compiles the growth cycle characteristics for the reference series in Table 1 of the file ResultsNameOfReferenceSeries.xls (in our example: ResultsIndustrialProduction.xls):

With the turning points (integrated manually or automatically), the procedure compiles the phases of the reference series, summarised in this table. For each cycle, the information given are the phases of expansion and slowdowns, the duration of each phase and cycle and the amplitudes of each phase and cycle.


2.2.2. Quarterly series

As CLIs process is on a monthly basis, the procedure changes a quarterly series into a monthly one by interpolation using the growth rate between two quarters and applying the third root of this growth rate to the quarter. Before this, you must define to which month the quarter refers using one of the four following possibilities:

� Quarter refers to first month of the quarter. � Quarter refers to the second month of the quarter (no extrapolation). First month before the

reference month of the quarter (the second) is extrapolated. � Quarter refers to the second month of the quarter (with extrapolation). Same than the preceding

method except that after the last data, one month (the third month of the last available quarter) is extrapolated.

� Quarter refers to the third month of the quarter. The two months before the reference month of the quarter (the third) are also extrapolated.

Thus, the software asks you to enter the reference month for the quarter as follows:

For a quarterly reference series, the method used is always the third one (quarter refers to the second month of the quarter (with extrapolation)).

At the end of the procedure, the quarterly series has be changed into a monthly one and the turning points have been converted onto a monthly basis taking into account the reference month of the quarter.

If a reference series is a quarterly series, the series is automatically transforms on a monthly series using the method “Quarter refers to the second month of the quarter (with extrapolation).


2.2.3. Manual turning points

Trend4.exe is the program which compiles the turning points on an automatic way. But it is also possible to enter the turning points manually (this method is used at the OECD). Here are all the steps when entering the turning points manually:

First of all, you click on the button Launch Complete Study and you select the series or all series. In our example, let us take the series BSProductionFT. You should enter the characteristics of the first turning points, whether it is a peak or a trough. Click on the good option:

When you click on either a peak or a trough, the “Input Turning Points” option becomes available. By clicking on it, the software asks you to enter the dates for all input turning points. The format should be mm/yy for a monthly series (September 1976 in our example below) and qq/yy for a quarterly series:

Once all turning points have been typed, press the button enter on your keyboard in order to finish the compilation.


When the turning points are entered manually, an Excel file is automatically created in the sub-directory corresponding of the series you are working with and the name of this file is “NameOfSeriesTPfixed.xls”. For example below, for the series BSProductionFT, the file BSProductionFTTPfixed.xls is created under the sub-directory C:\OECD_CACIS\OECDExample\BSProductionFT. Let us see the structure of this file:

The name of the file is BSProductionFTTPFixed.xls. In the first column, there is either P (for peaks) or T (for trough). In the second column, are the years and in the third column are the months. Now, if you do not change the option form Manual turning points to Automatic turning points, Trend4.exe will take all the time the turning points of this file. If you want to change the date of a turning point, add turning points, delete turning points, do everything in this file.

2.2.4. Turning points with Hodrick-Prescott

The Hodrick-Prescott method has been included in the software for short-term time series. As PAT could not compile if series do not have more than 99 data points for a monthly series and 25 for a quarterly series and/or do not have more than 4 turning points, the Hodrick-Prescott method is then used. This is the reason why the long-term trend and the business cycles for each series are calculated by Demetra using the Tramo/Seats program with trend and cycle options for the Hodrick-Prescott filter (see section 1.3).

Demetra compiles the long-term trend and the business cycle series. There is no automatic procedure (like with PAT) to compile automatically the turning points. The business cycle series is a time series moving around 0. So, a peak is defined when a maximum is found after a trough and vice versa (it is the maximum inside a time period where the business cycle series has crossed the 0 line). This procedure of determining turning points has not been implemented yet and because of that, the user of the software must define the turning points by him-self and verify first the turning points detected by the procedure.


Let us take the example of the series NewCarRegistrations. First, Launch complete study for the series. A first box appears and asks if you want to launch the complete study (usually used when it is the first time you run the normalisation in order to have a first selection of turning points) or the Study After Selecting the Turning Points by the user (step where the user has definitively defined the turning points of the series):


For the first time, you run this procedure you must choose “Entire Study” in order to have a first compilation and approximation of the turning points. In the sub-directory C:\OECD_CACIS\OECDExample\3_ NewCarRegistrations, a new Excel file has been created and is called NewCarRegistrations CheckTP.xls. In this file, the original series, the long-term trend, the business cycles and the turning points have been compiled (the file has exactly the same structure as with a normalisation with PAT). There are also two graphs, one with the original series and the long-term trend and the second one with the ratio to trend series and the turning points. Let us have a look to the structure of the file:

At the bottom, you have the list of turning points. In this list, you must select the ones you want to delete and destroy the line referenced to the turning point to be deleted (of course you must delete the turning points two by two because you always must have a trough following a peak and vice versa). When the turning points have been definitively selected, run the procedure and choose the option “Study after Selecting the Turning Points”.


2.2.5. The Results file

This file is where you have all the results for each reference series. The file is under C:\OECD_CACIS\OECDExample\1_RefNameOfReferenceSeries\Results and is called ResultsNameOfReferenceSeries.xls. This file contains six sheets:

� Table 1 includes the characteristics of the growth cycle of the reference series � Table 2 includes a first set of characteristics of components compared to the reference series

(Period, MCD, Mean Lead at turning points, Median lead at turning points, Standard deviation, Cross correlation)

� Table 2Bis includes a second set of characteristics of components compared to the reference series (Number of turning points over common sample period, extra turning points, missing turning points, Extra/missing turning points in % of TP in reference series, Turning points leading by 2 or more periods, Turning points leading by 2 or more periods in % of TP in reference series, Quadratic probability score)

� Table 3 includes a first set of characteristics of composite indicators compared to the reference series (Period, MCD, Mean Lead at turning points, Median lead at turning points, Standard deviation, Cross correlation)

� Table 3Bis includes a second set of characteristics of composite indicators compared to the reference series (Number of turning points over common sample period, extra turning points, missing turning points, Extra/missing turning points in % of TP in reference series, Turning points leading by 2 or more periods, Turning points leading by 2 or more periods in % of TP in reference series, Quadratic probability score)

� SummaryClis includes the list of the created composite indicators with the options start year, type of composite indicators, component series

2.2.6. Implication in the directories

After the normalisation of each series, a number of files are created in each series directory. The files depend on the de-trending method selected. When the de-trending method is PAT, the following files will be found, example for BSProductionFT (with the manual turning points option on):

� BSProductionFT.xls: input data file � BSProductionFTNorm.xls: output data file with all series until normalised series � BSProductionFTTPFixed.xls: File with input turning points � BSProductionFT.txt: input data file created before launching Trend4.exe � Output.dat: output file after Trend4.exe includes compiled data (Original data, long-term trend

and turning points) � Output.txt: log file explaining all step for the compilation of output series


2.3. “Change Options to Indicators” procedure

This button permits to change some options to the study, to see which series are included in the study or to add new components:

This button has four possibilities. By clicking on it, it appears the four following options:

Let us see know these different possibilities:


2.3.1. View and Change Options

By clicking on this button, the following box appears and permits to change any options you want (the screen is in white whereas when you enter for the first time the options, it was in dark grey):

You can change every option you want. The button “Input Turning Points for All Series” permits to change the options “Turning points” from Automatically to Manually for all series.

If you change a component indicator into a reference indicator, you must re-run the step 2. Launch Complete Study.


If you want to change a reference series into a component series and if it is the only reference series you have, the following message will appear:

By clicking on Exit, you stop the procedure of changing options and the reference series keeps being the reference series. By clicking on Back, you go back to the “View and Change Options”.


2.3.2. Series in the study

This button lists the indicators you are working with. They are separated in two categories - reference series and component series:

In the study, there are two reference series and six component series.


2.3.3. Change beginning date

It can be necessary to change the beginning date if for example the beginning of the series disturbs the determination of a good long-term trend. By clicking on this button:

This procedure creates a new excel file in the sub-directory of the series (C:\OECD_CACIS\OECDExample\3_ConsumerSentiment) which is ConsumerSentimentAllPeriod.xls in case you want to change again the beginning date.


2.3.4. Add component(s)

This procedure permits you to add components in the analysis. The structure of the file must be the same than for the first files. You must do the seasonal adjustments with Demetra and keep the long-term trend and the business cycles with Hodrick-Prescott. When clicking on the button, it opens automatically the “Select One File To Open” box. After selecting the input file, the general options box for each indicator appears:

The new input has been saved in the folder C:\OECD_CACIS\OECDExample\4_OriginalData and the new sub-directories for the two new series have been created (SharePrices and StocksRawMaterialsFT).


2.4. “Graph of turning points procedure” procedure

You can have a look to the results of normalisation on a graph. Two graphs can be seen:

� Ratio to trend graph with turning points � Long-term trend graph with original series

If we look at the GDP series:

It is also possible to print either the current graph (graph on the screen) or all ratio to trend graphs or all long-term trend graphs.


If you try to graph the turning points of a series which have not been compiled for normalisation, the following message appears. By clicking on OK, the box disappears.

2.5. “Compilation of Statistics” procedure

After preparation of the series, the next step is to analyse the series one by one and finally to select of series for a composite indicator. In order to select the best series, we have three tools:

� Graphs � Cross correlation � Statistical board (called StatBoard) – First part


When you click on the button “4. Compilation of Statistics”, the following box appears and you have to choose first the reference series (possibility of selecting one by one or all reference series at the same time), then the component series (possibility of selecting one by one or all component series at the same time and finally the statistics (possibility of choosing either graphs or cross correlation or statboard or all at the same time):

Each time you run this procedure there is a checking in order to see if the compilation can be done. For each series, the normalisation must have been done. If not, a message saying that either a reference series or a component series has not been treated. You must run the “2. Launch Complete Study” procedure for the series not treated. Here is an example for the component series SharePrices:

2.5.1. Graphs

This tool allows you to plot the ratio to trend series of the component series against the reference series in order to compare the cycles of the component series with these of the reference series. The normalised series are used. A new Excel file is saved in the “4_Graphs” sub-directory under the sub-directory of the reference series (Ex: C:\OECD_CACIS\OECDExample\1_RefIndustrialProduction\Graphs when the reference series is IndustrialProduction) and is called GR_NameOfSeries (in our example, the file is called GR_ConsumerSentiment.xls).


2.5.2. Cross-correlation

This procedure allows you to calculate the cross correlation between the component series and the reference series. It takes the smoothed series for both series. It creates a new excel file in the directory “4_CrossCorrelation” which is called CC_NameOfSeries.xls (in our example, the file is called CC_ConsumerSentiment.xls) under the directory of the reference series (Ex: C:\OECD_CACIS\OECDExample\1_RefIndustrialProduction\Graphs when the reference series is IndustrialProduction).

This procedure puts two new statistics in Table 2 of the file ResultsNameOfReferenceSeries.xls, the lead / lag and the coefficient of cross correlation.


2.5.3. Statistical board (called StatBoard)

This procedure allows you to calculate a set of statistics about the turning points of the component series that are compared to the turning points of the reference series. These statistics are reported in two different sheets (Table 2 and Table 2Bis) in the file ResultsNameOfReferenceSeries.xls and are:

� Mean lead at turning points (for peaks, troughs and all turning points) in table 2 � Median lead at turning points (for peaks, troughs and all turning points) in Table 2 � Standard deviation in Table 2 � Number of turning points over common period sample in table 2Bis � Extra turning points in Table 2Bis � Missing turning points in Table 2Bis � Extra/Missing turning points in % of turning points in reference series in Table 2Bis � Turning points leading by 2 or more periods in Table 2Bis � Turning points leading by 2 or more periods in % of TP in reference series in Table 2Bis � Quadratic Probability Score (QPS) in table 2Bis This procedure must be done in two steps. The first step is the creation of the files needed for the compilation of the statistics. It has created in the sub-directory “StatBoard” under each reference series sub-diretory two new Excel files called SB_NameOfSeries.xls and SB_NameOfSeriesFinal.xls. In our example, they are called SB_ConsumerSentiment.xls and SB_ConsumerSentimentFinal.xls as below:

2.6. “Compilation of Final Statistical Boards” procedure

This is the second step of the compilation of the statistical board statistics. After having created the two files for each series, you must prepare the file for the second step i.e. you must match the cycles of the component series with the cycles of the reference series.

Open the file SB_ConsumerSentiment.xls in Excel and arrange the cycles and phases of the series with the reference series. Here is the explanation on how to proceed at this step.

We have all turning points for the reference series and the series selected (ConsumerSentiment). As we can see, the first cycle for the component series does not match with the first cycle of the reference series. So we have to shift to the right the component series turning points until the first turning of the


reference series that matches with the first one of the component series (Important: you must match a peak with a peak and a trough with a trough) as follows:

For the example, we hided the columns B to M (just for the example) because the first turning point for the series Consumer Sentiment begins in 1990 whereas the first turning point of the reference series begins in 1963.

We notice that the series ConsumerSentiment as an extra cycle that cannot be seen in the reference series. This process of shifting and removal must be repeated for all turning points.

When you finish this very important step, save the file and close it, and then click on the button “5. Compilation of Final Statistical Boards”. The following box appears and you have to choose first the reference series (possibility of selecting one by one or all reference series at the same time) and then the component series (possibility of selecting one by one or all component series at the same time:

By clicking on “Compile Final Statistical Boards”, the procedure updates seven new statistics in Table 2 (first table below) and eight new statistics in Table 2Bis (second table below) of the file ResultsNameOfReferenceSeries.xls (in our example, ResultsIndustrialProduction.xls).


Here are the results in Table 2Bis:

All these statistics are explained in the glossary in annex.

2.7. “View of Final Cyclical Analysis Results” procedure

This permits to view automatically series by series, the results that have been compiled in the preceding procedures.


On the right of the user form, there are three possible printing functions:

� Print Current Graph prints the graph of the reference series and the component series (ratio to trend series) which is on the screen.

� Print All Graphs prints all graphs (ratio to trend series) for the reference series selected of all component series.

� Print Results for All Series prints the results for the reference series of all components series, in total two tables which are Table 2 and Table 2Bis.

2.8. “Go to COMPOSITE INDICATOR SYSTEM” procedure

When you have finished the cyclical analysis part, click on the yellow button “Go to Composite Indicator System”:

By clicking on this button, the cyclical analysis part will disappear and the composite indicator system part (in yellow) will appear.


3. COMPOSITE INDICATORS

After having done the cyclical analysis study on reference series and all potential components, we have to construct composite indicators - leading, coincident or lagging composite indicators. The composite indicator study proceeds as follows:

The composite indicator system part is composed of six different steps:

1. Create a New Composite Indicator 2. View of a Created Composite Indicator 3. View of Turning Points 4. Compilation of Statistics 5. Compilation of Final Statistical Boards 6. View of Final Composite Indicators Results

It is possible to come back to the cyclical analysis part by clicking on the button “Back to Cyclical Analysis”.


3.1. “Creation a new Composite Indicator” procedure

The detection of turning point is always done by the PAT method (with TREND4.exe).

It is not possible to create for any reference series more than 99 composite indicators. By clicking on the button, the following box appears:

By clicking on “Run New Composite Indicator”, the following window appears:


At this point, some options must be chosen in order to have the button “Run Composite Indicator” available:

� Beginning year: it refers to the beginning year of the composite indicator. The years that can be selected begin in 1955 until now. The option Automatic lets the software compile the composite indicator from the first available year.

� Nature of CI: you have to select between the three following possibilities: Leading, Coincident and Lagging.

� Component Indicators Included in the Composite Indicator: On the left, there are all the component series available. Click on each indicator you want to be a component of the composite indicator (you can select several indicators using the key Ctrl) and used the right arrow in order to include the indicator in the right box. If you want to get off an indicator of the composite indicator, select the indicator in the right box and click and the left arrow.

For example, we want to compile a composite leading indictor with all the series except the indicator GdpComponent and the software will decide automatically the beginning date of the composite leading indicator.


When all necessary options are selected the button “Run Composite Indicator” becomes available and the Composite Indicator title has been changed automatically when the option Nature of CI has been selected (in our example: Leading).

By clicking on “Run Composite Indicator”, the software asks you to enter the percentage restriction (the OECD rule is 60%) which is the percentage of needed components in order to compile the composite indicator:

After having chosen the percentage restriction for the compilation of the composite indicator by clicking on OK (if you do not enter any percentage, the software will automatically take as percentage restriction 60%), the software asks you if you want the composite indicator turning points to be compiled automatically (Automatic Turning Points) or manually (Input Turning Points):

The creation of a new composite indicator implies a change in the structure of the project:

A sub-directory (Cli1) has been created under the sub-directory of the reference series we have chosen at the beginning (IndustrialProduction) and all created files are:


� CC_Cli1.xls: it includes the compilation of the cross correlation between the reference series and the composite indicator.

� Cli1.txt: it is the txt file before running TREND4.exe in order to compile turning points of the composite indicator.

� Cli1.xls: it includes the input file with the calculated composite indicator – amplitude adjusted corrected with MCD coefficient.

� Cli1_Comp.xls: it includes the compilation of the normalised composite indicator with all the indicators which compose it.

� Cli1_Ref.xls: it includes the references series and composite indicators series. � GR_Cli1.xls: it includes the graph of the reference series and composite indicator (ratio to

trend series) � Output.dat: output data file after TREND4.exe. � Output.txt: Log file to see all the calculation process. � SB_Cli1.xls: it includes the statistical board preparation for the compilation of the statistical

board statistics. � SB_Cli1Final.xls: it includes the statistical board results.


3.2. “View of a Created Composite Indicator” procedure

This button gives the possibility of having a look to a special composite indicator and the possibility of changing some options (Beginning date, Nature of CI and Components) to the composite indicator:

You must select the reference series first then the composite indicator and the rest is automatically updated. Then you can change the options and finally run the composite indicator or close. When you click on “Run Composite Indicator”, the steps are as if you were creating a new composite indicator (percentage restriction and automatic or input turning points).


If you select a reference series and no composite indicator has been created for this reference series, the following message appears:

3.3. “View of Turning Points” procedure

By clicking on the button, the following box appears. You have first to select the reference series (if there are more than 1 reference series) and then the composite indicator. The graph appears and you have the possibility of printing it:


If no composite indicator has been created for a reference series, the following message appears:

3.4. “Compilation of Statistics” procedure

This procedure compiles the cross-correlation statistics and prepares the statistical board files for the selected composite indicator (graphs is compiled automatically):

Here are the steps for the compilation of statistics:

1. Select the reference series: if you have only one reference series, the software will select automatically.

2. Select the composite indicator: if you have only one composite indicator, the software will select it automatically.

3. Select the statistics: you can select either the cross correlation statistics or the statistical board statistics or both statistics. Here, the graph is compiled at the first procedure “Creation of a New Composite Indicator”. And it is not possible to compile these statistics for all composite indicators at the same time it must be done one by one.

4. Launch the Statistic Compilation procedure.


If you want to compile the statistics for a composite indicator and, if no composite indicator has been created for a reference series, the following message appears:

3.5. “Compilation of Final Statistical Boards” procedure

It is necessary to calculate the StatBoard statistics for the composite indicators. To compile the statistical board for composite indicators, you must go back to the StatBoard paragraph in cyclical analysis phase (see 2.5.3. Statistical board (called StatBoard)). When the file is restructured (it is only possible to compile the statistics for one composite indicator at the time), click on the button “Compilation of Final Statistical Boards”:

After having selected first the reference series and then the composite indicator, click on “Compile Final Statistical Board” for the calculation.

If you want to compile the final statistical board statistics for a composite indicator and, if no composite indicator has been created for a reference series, the following message appears:


3.6. “View of Final CI Results” procedure

This procedure gives the opportunity of having all results of a composite indicator compared to reference series:

There is the possibility of plotting different graphs:

� Ratio to trend graph between the reference series and the composite indicator � Trend restored graph between the reference series and the composite indicator � 6-month rate of change of the composite indicator

It is also possible to print:

� The current graph on the screen � The composite indicator results


If you want to see the results and no composite indicator has been created for a reference series, the following message appears:


ANNEX: THE PHASE-AVERAGE TREND PROGRAM – OECD VERSION 4 (2003)

Objectives

The objective of the Phase-Average-Trend (PAT) program is to jointly calculate the long-term trend and to determine the turning points (peaks and troughs) in a seasonally adjusted time series.

The program accepts prior estimates of turning points.

Program Outline

The major operations of the program are as follows:

� Calculation of a tentative long-term trend. This is a 75-month moving average of seasonally adjusted data. The first and last 37 observations backcast and forecast by extrapolation using the rate of change between the average of the first (last) 75 months starting two years later (earlier). If the trend-adjustment option is switched off this step is skipped.

� Determination of tentative turning points in the series corrected for the long-term trend using the “Bry-Boschan” routine (see details in section 1.3). (If the trend-adjustment option is switched off turning points are determined using the input data not using the data corrected for long-term trend. This gives “classical cycles” instead of “growth cycles”).

� Calculation of the Phase Average Trend (see details in section 1.4) with the tentative turning points as input and calculation of deviation from this final long-term trend.

� Determination of final turning points using the Bry-Boschan routine (section 1.3) with de-trended data calculated in previous step as input.

Turning Points Selection

The turning points selection is based on the Bry-Boschan technique. First major cyclical swings in a series are identified then areas of cyclical maxima and minima, and finally turning points are determined.

Tests are performed to eliminate:

� Turns within 6 months of the beginning and end of a series; � Peaks (troughs) at both ends of the series which are lower (higher) than values closer to the end; � Cycles shorter than 15 months; � Phases shorter than 5 months;

The turning points identified are the tentative turning points.


Long-term trend estimation

The tentative turning points are used as input for the calculation of the Phase-Average-Trend (PAT). The tentative turning points are used to break up the original series into phases. This means that the PAT is a trend that allows for different lengths of successive cyclical phases, defined as the distance between two successive turning points. The trend is then interpolated between the centered values of the averages of the data within these phases, and the program selects turning points in the deviations of the raw data from the final trend.

Detailed program steps

The entire procedure is as follows: 1. Calculation of tentative trend: a 75 month moving average of seasonally adjusted data. The trend is

extrapolated to give the first and last 37 observations. The extrapolation is performed by using the rate of change between the average of the first (last) 75 months starting two years later (earlier).

2. Calculation of deviations (ratios or differences) of individual observations from tentative trend. 3. Determination of tentative cyclical turning points and thus expansions and contractions, in

deviations. 4. Calculation of phase averages (i.e. averages during cyclical phases) of original seasonally adjusted

data, for all expansions and contractions. 5. Calculation of three-term moving averages of phase averages (triplets). 6. Calculation of "slope" of second approximation of trend by connecting mid points of triplets. 7. Adjustment of "level" of trend, to match the original series, by making the sum of each segment

between two consecutive triplets equal to the sum of the original observations during that period in time.

8. Extrapolation of trend by calculation of slope from first (last) triplet midpoint so that the trend

values of the first (last) segment are equal to the sum of the original observations. 9. Calculation of twelve month moving average of the second approximation of trend to yield the

final trend. 10. The last stage of the program, the identification of definitive turning points, is carried out, using the

final trend as input to the Bry-Boschan routine for selection of cyclical turning points.

Installation

Create a sub-directory under your C:\ drive called C:\OECD_CACIS Copy TREND4.EXE and PAT.xls under this sub-directory.


Input data file

A data file contains the data from one series. Here is an example of the input file (open in Excel but the program creates it as a text format file):

The data file used as input to the program must have the following format: 1st line of record (parameters):

Field Length (characters)

Comments

Series ID Series Identifier Periodicity 1 1 = Monthly data

2 = Quarterly data Deviation from trend option 1 0 = ratio

1 = difference Turning point input 1 0 = Turning point dates are contained in

data file 1 = Turning point dates are calculated

Detrending Option 1 0 = De-trending 1 = No de-trending (raw data)

Printout Option 1 0 = short printout 1 = normal printout 2 = long printout 3 = extra long printout

Number of years of data 2 Number of years/lines of data that follow

N.B.: 1. This record is required. 2. The ‘series identifier’ is not validated. 3. If ‘turning point input’ is contained in the data file (value 0), the ‘detrending option’ MUST be set

to “detrending” (value 0). 4. The ‘Printout Option’ determines the contents of text file output. 5. The ‘Number of years of data’ must match the number of years worth of data that follows for the

series.


2nd line of record (Title of the series as it will appear in the output text file):


Comments

Series ID max. 78 Series title as it is to be printed in the output text file

N.B.: 1. This record is required. 2. The contents of the record are not validated.

3rd & 4th lines of record (Turning Points):

3rd line Field Length

(characters) Comments

Peak/Trough indicator 1 Indicates whether the first date is a peak or a trough P = peak (optional) T = trough

Period 2 Period in which the turning point occurs. 01 to 04 for quarterly data 01 to 12 for monthly data.

Year 2 Year in which the turning point occurs. Continuation character 1 Indicates whether or not more turning

points are to be input ‘&’ – more turning points follow on the next line

4th line


Comments

Space 1 Period 2 Period in which the turning point occurs.

01-04 for quarterly data 01-12 for monthly data.

Year 2 Year in which the turning point occurs. N.B.: 1. These records are optional, depending on the Turning point input option selected in the first

record. If the turning point option is set to “input from data file” (value 0), then at least record 3 must exist.

2. Up to 17 turning points (period and year) can be entered on each of records 3 and 4. As many as possible must be entered on record 3. Record 4 exists only if there are more than 17 turning points in total.

3. The turning points must be given in chronological order.


5th line and subsequent of records (data values from the series):


Comments

Year 4 The year to which the data refers. Figure xxxxx.xx The figure from the series. N.B.: 1. For quarterly data, there will be four figures for each year held in each line. For monthly data,

there are 12 figures for each year. 2. There must not be any empty cells or zeroes within the input series. If the data for the final year is

incomplete, complete the record with spaces so that it is the same length as other years of same series in the file.

Output

Output files

Two output files are produced. The first is a data file containing the computed final trend (if the extra long printout option has been selected) and the final turning points for each series. The second is a report, showing the same information along with intermediate results.

Each output file contains the results of all series contained in the input file.

The two output files are created in the same directory as that in which the program runs and the input file resides. They are named:

OUTPUT.TXT (report file)

OUTPUT.DAT (data file).

Remark: In one case, the two files are empty. It is when you select to input manually the turning points and when you decide not to de-trend the series. In that case, if the files have not been already created, it creates two empty files. If the files were already created, delete them in the Explorer.

Printing the report

The output report must be printed in landscape format, and using a fixed-pitch font such as courier (NOT proportional fonts such as helvetica or times roman).

Under Word:

Select the whole report (Menu “edit”, option “select all”). Set the page format to Landscape (Menu “file”, option “page setup”, “paper size”, “landscape”). Ensure that a fixed-pitch typeface, such as courier (suggested size 8), is used. Under other word-processing software, the same constraints apply.


Common problems

� Ensure that the input data file exactly matches the input file specification. This is the main

reason for problems.

� Ensure that the input file is in the same directory as the program file.

� Look at the output report (OUTPUT.TXT). If there is a problem with the data contained in the series, it will be indicated here.

� You cannot have as last figure a 0 (even if you have transformed it as said before). Just delete it or do an estimation for the following month or quarter.


GLOSSARY

Amplitude adjustment

The composite indicator is adjusted to ensure that its cyclical amplitude on average agrees with that of de-trended reference series.

Business cycle

Business cycles are recurrent sequences of alternating phases of expansion and contraction in the level of a time series

Composite Leading Indicator (CLI)

CLI is an aggregate time series displaying a reasonably consistent leading relationship with the reference series for the macroeconomic cycle in a country. CLI is constructed by aggregating together component series selected according to the criteria specified in component series. However, It is important to emphasize that component series are not selected according to a strict quantitative criteria based on the cross-correlation with the reference series. Thus, CLI can be used to give an early indication of turning points in the reference series but not for quantitative forecasts.

Component series

Component series are economic time series which exhibit leading relationship with a reference series at the turning points. Their seasonally adjusted or raw form is combined into a composite indicator (which can be lagging, coincident or leading). The component series are selected from a wide range of economic sectors. Selection of the appropriate series for each country is made according to the following criteria: Economic significance: there has to be an a-priori economic reason for a relationship with the reference series;

Cyclical behaviour

Cycles should lead those of the reference series, with no missing or extra cycles. At the same time, the lead at turning points should be homogeneous over the whole period. Data quality: statistical coverage of the series should be broad. Series should be compiled on a monthly rather than on a quarterly basis. Series should be timely and easily available. There should be no break in time series. Series should not be revised frequently.

Cycle

The time span which separates two turning points of the same nature (two peaks or two troughs).


Growth cycle

Growth cycles are recurrent fluctuations in the series of deviations from trend. Thus, growth cycle contractions include slow-downs as well as absolute declines in activity, whereas business cycles contractions include only absolute declines (recessions). The OECD cyclical indicator system uses the "growth cycle" approach.

Months for Cyclical Dominance (MCD)

MCD is defined as the shortest span of months for which the I/C ratio (I: Irregular and C: Cycle) is less than unity. I and C are the average month-to-month changes without regard to sign of the irregular and trend-cycle component of the series, respectively. There is a convention that the maximum value of MCD should be 6. For quarterly series, there is an analogous measure, quarters for Cyclical Dominance (QCD), which has a maximum value conventionally defined as 2.

Normalisation

This transformation of the de-trended component series is required prior to aggregation into the composite indicator in order to express the cyclical movements in a comparable form (i.e. for either a multiplicative or an additive model when estimating the trend); the cyclical amplitude is homogenised. The method used to calculate normalised indices is to subtract the mean from the observed value and then to divide the resulting difference by the mean of the absolute values of the difference from the mean.

One-month percent change

The 1-month percent change is defined as the month-to-month change in the trend restored composite indicator. This gives an indication of the most recent changes in the indicator. A change in the direction of the indicator or a continued inflection in the rate indicates a turning point. In practice, a 3-month rule can be applied for the identification of a turning point. That is, three consecutive months of negative/positive change will give a signal for a peak/trough.

Phase

Time span between a peak and a trough.


Quadratic Probability Score (QPS)

The QPS statistics is a quantitative measure of its performance in predicting turning points. The QPS is given by:

N

RPQPS

N

ttt

HH��

�� 1

2

],[

)(221

In the equation above, P denotes predicted outcomes from a candidate leading indicator and R observed realisations in the reference series, both equal to one for a turning point and zero otherwise. N is the total number of sample observations. By construction, the value of QPS ranges between 0 and 2 with O indicating perfect prediction and two indicating no single correct signal from a candidate leading indicator. [H1 , H2] is the prediction window, which is used to determine whether a predicted outcome represents a correct signal or a false one when is it takes the value of one, and whether or not it has missed a turning point when taking the value of 0. This can be illustrated in the following matrix: A TP occurs within [H1 , H2] No TP occurs within [H1 , H2] Signal (P=1) Correct signal (A) False signals (B) No signal (P = 0) A TP is missed (C) Correct predictions (D) If we assume that H1 = 4 months and H2 = 12 months, then a signal issued by a leading indicator in a particular month will be considered a correct (a false) signal, denoted as A (or B0, if a (or no) turning point in the reference series occurs within 12 months or has occurred within previous 4 months. Similarly, if no signal is issued by the leading indicator in a particular month, it will be considered having missed a turning point (or a correct prediction), denoted as C (or D), if a (or no) turning point actually occurs within next 12 months or has occurred within previous 4 months. This study chooses [4 , 12] as the prediction window on the basis of visual inspection of relative movements in the reference series and candidate leading indicators.

Ratio to trend

The trend is eliminated from the series by dividing the original series by the trend to give a ratio-to-trend since the underlying structure of most series used is multiplicative. For series whose underlying structure is additive, a difference-from-trend series is calculated.


Reference series

Cyclical indicator systems are constructed around a "reference chronology". The reference series is the economic variable whose cyclical movements it is intended to predict. In the OECD system, the index of total industrial production is used as the reference series. Ideally, Gross Domestic Product (GDP) would be used as the reference series, but for many countries, there is often a substantial time lag in the publication of GDP estimates and they are usually available only on an annual or quarterly basis. Industrial production constitutes the more cyclical part of the aggregate economy and the cyclical profiles of industrial production and GDP have been found to be closely related, so that cyclical indicators identified against industrial production serve well as indicators for the GDP cycles.

Six-month rate of change

The annualised 6-month rate of change of composite indicators is calculated by dividing the figure for a given month m by the 12-month moving average centred on m-6.5. It is easier for users to interpret the annualised 6-month rate of change since the volatility in the composite indicator has been smoothed out. At the same time, the annualised 6-month rate of change provides earlier signals for the turning points. Let Tt and Ct be respectively the 6-month rate of change and the composite indicator at t,

100112

5.612

12

11

��

�

�

��

�

��

��

iCt

CtTt

Smoothing

Component series are smoothed according to their MCD (months for cyclical dominance) values to reduce irregularity.

Trend

In time series analysis, a given time series can be decomposed into: - A cyclical component, - A trend component, - A seasonal component, - An irregular component, The method of trend estimation adopted by the OECD is a modified version of the Phase-Average Trend (PAT) method developed by the United States NBER.

Trend-restored

This form of the composite indicator is calculated by multiplying the amplitude-adjusted and the ratio-to-trend composite indicator by the trend of the reference series to obtain the trend restored composite indicator. This trend-restoration enables direct comparison with the reference series.

Turning point

In the growth cycles analysis, a turning point occurs in a series when the deviation-from-trend series reached a local maximum (Peak) or a local minimum (Trough). Growth cycle peaks (end of expansion) occur when activity is furthest above its trend level. Growth cycle troughs (end of contraction/recession) occur when activity is furthest below its trend level.

Documents

oecd cyclical analysis and composite indicators system